Wikipedia:Reference desk/Archives/Science/2008 March 16

= March 16 =

Toxicity of non-stick pan lining?
I know it's not the recommended methd of cleaning them, but I often use rough scrubbing pads on my cheap no stick pans. The coating does flake off slowly. If I am ingesting this material in small quantities, should I be worried?--68.237.2.101 (talk) 03:15, 16 March 2008 (UTC)


 * See Polytetrafluoroethylene. Basically if it's Teflon and hasn't been overheated it is chemically inert and should pass straight through your body. --antilivedT 03:42, 16 March 2008 (UTC)

I personally develop a bad skin condition whenever I eat something cooked in Teflon, so it can't be entirely harmless. And no overheating is not the issue. Dupont has a vested interest in having you believe their stuff is safe if used properly, so what they tell you cannot be trusted.

If I were you I'd err on the side of caution and get some regular cookware -- stainless steel, cast iron, copper if you're wealthy. But it really depends on how concerned you are about your health and whether doing a little extra scrubbing to clean normal cookware is something you'd be willing to do. If you aren't a big-time health nut it's probably not something you need to worry about. Vranak (talk) 15:20, 16 March 2008 (UTC)


 * This is a contentious issue, and as far as I know there isn't a definitive answer yet. As Vranek notes, the manufacturer has a vested interest, so don't believe everything you hear.
 * Here are the facts as I understand and observe them:
 * Teflon and related compounds are quite biologically inert; they'll pass through you like a rock.
 * "Burnt" Teflon is reasonably nasty, and is to be avoided.
 * The non-stick coating on non-stick pans does flake off. More so with cheap pans.
 * The non-stick coating is much more likely to flake off it it's been overheated, i.e. burned. Danger, Will Robinson.
 * The non-stick coating is easily damaged (and made much more prone to both burning and flaking) by the use of metal implements, either while cooking or cleaning.


 * My own conclusion is that the potential toxicity of burnt-and-flaked-off Teflon is suitably worrisome that it's worth avoiding.


 * If you want to clean your cookware so vigorously that the non-stick coating flakes off, pretty soon it isn't non-stick any more, and you might as well use non-non-stick cookware, instead. Then you don't have to worry.


 * Personally, I don't like non-stick cookware, because I can't be bothered to be careful of it. (Plastic spatulas are teh pitz; they melt if you leave them in.)  I find that with proper cooking techniques, my ordinary (non-non-stick) cookware doesn't stick badly enough to worry about.  YMMV. —Steve Summit (talk) 15:36, 16 March 2008 (UTC)


 * Also, steel wool is absolutely indispensible for regular cookware. Vranak (talk) 17:00, 16 March 2008 (UTC)


 * Who uses plastic spatulas? Silicone or wood are much better Nil Einne (talk) 07:30, 18 March 2008 (UTC)


 * And why would you use steel wool on a non-stick pan ? It's guaranteed to destroy it.  You might as well polish your car with steel wool. StuRat (talk) 17:31, 16 March 2008 (UTC)


 * I said it's good for regular cookware. i.e. non-non-stick cookware. Vranak (talk) 19:33, 16 March 2008 (UTC)


 * Right. I wasn't replying to you; please note the indentation.  Apparently the OP is also using steel wool, or something just as bad, on non-stick pans. StuRat (talk) 22:39, 16 March 2008 (UTC)


 * Well, a rough scrubbing pad could mean many things. What matters more than the roughness is the abrasiveness. If the grit in the scrubbing pad is too hard, it will scratch the teflon.  The OP may want to invest a non-abrasive nylon scrubbing pad.  Or switch to Cast-iron cookware, which has the benefit of improved heat retention. Dforest (talk) 21:44, 17 March 2008 (UTC)


 * (edit conflict)Hi. I've watched infomercials on TV way too often, and on one of them, there is a solution to all your problems: SmartWare. Try Googling it or something. Remember, this offer is not avalible in stores. Don't delay, order your SmartWare today! Call within the next 30 seconds and recieve my special bundt cake pan, as well as our cake stencil: Turn a ho-hum cake into a yum-yum cake! You should have at least two to three bowel movements a day. Less than one bowel movement a day is irregular, and can lead to constipation. (Dr. Ho) Hope this helps. Thanks. ~ A H  1 (TCU) 19:39, 16 March 2008 (UTC)


 * Yes, it seems as if infomercials are full of Ho's selling crap. StuRat (talk) 22:41, 16 March 2008 (UTC)

Horizontal search functions (in visual perception)
Does anybody have a clue what could be meant by the expression horizontal search functions in the following sentence: "Targets that yield horizontal search functions are assumed to reflect visual primitives, the basic building blocks of perception." (PS this is a sentence in my textbook, not a sentence found in Wikipedia.) Lova Falk (talk) 15:11, 16 March 2008 (UTC)


 * It's just a guess, but they may refer to a heirarchy of objects, like the following example:

Humans |   | Men  Women |  |    Barb  Sue


 * So, a horizontal search would be a search at the same hierarchy level. For example, "Is that Barb ?", "No", "Then is that Sue ?", etc. StuRat (talk) 17:26, 16 March 2008 (UTC)
 * This sounds very close to a classification project I was working on. In my project the term "horizontal" was used literally to suggest the conjunctive sense of "and" when a glyph was used as a modifier of another glyph. "Vertical" on the other hand was used to suggest the conjunctive sense of "or". Thus a word is considered a "horizontal" set of glyphs and a sentence is then a horizontal set of words, whereas alternate glyphs, words, phrases, and sentences are deemed "vertical".

It would help if you gave us a little more background on the textbook and the section in question. One isolated sentence from any textbook is going to be hard to make sense of without context. Give us the whole paragraph and the title of the book, at least. Otherwise people are going to be just guessing blindly. --98.217.8.46 (talk) 18:12, 16 March 2008 (UTC)

Is Energy relative?
This is perhaps a very silly question, but nevertheless, it has troubled my from time to time. What's wrong with the following line of reasoning:


 * Velocity is relative (depends on the reference frame)
 * Therefore, its time derivative, acceleration is relative
 * Force, which is acceleration times mass, is relative (or, we can say, momentum and its rate of change are relative)
 * Thus, quantities like kinetic energy (m*v^2/2) and work (force x displacement) are also dependent on reference frame.

Is this last proposition correct? deeptrivia (talk) 16:02, 16 March 2008 (UTC)


 * Yes, but the second and third aren't. Acceleration isn't inherently a frame-dependent thing. A speedometer can only tell you the relative speed between two objects (for example, your car and the road), but an accelerometer can tell you its own intrinsic acceleration without reference to anything else. Inertial navigation is based on this principle. -- BenRG (talk) 18:37, 16 March 2008 (UTC)


 * So, there is such a thing as an absolute acceleration? If so, how can we ever find it? For example, the earth itself accelerates as it revolves around the sun, and the sun might be accelerating around the center of the galaxy. Is it that these effects are small, and in principle measurable? Do the sensors we use include all these accelerations? deeptrivia (talk) 21:16, 16 March 2008 (UTC)
 * Yes these small accelerations are absolute and measurable. The accelerations ,that are a direct consequence of the gravitational forces in the universe, are making the changes in velocity that make astronomical bodies orbit each other, rather than move in a straight line as they would do if no force operated on them. GameKeeper (talk) 23:16, 16 March 2008 (UTC)


 * It's a key tenet of general relativity that accelerations are not relative except that they can't be distinguished from gravitational fields. You can use an accelerometer to measure accelerations; the most simple of which is a cup of coffee. Start to accelerate it, just a little—you'll start to spill it. But if you have it in an inertial frame, no matter how fast you are going (say, 67,000 miles an hour), it'll sit there placidly.
 * Einstein used to comment that theory of relativity was something of a misnomer: what's important is not what is relative, but the very few things which are not relative, like the speed of light. It is from finding the few things which are not relative—and the implications of that—that the genius of his theory comes. --98.217.8.46 (talk) 00:59, 17 March 2008 (UTC)


 * KE and momentum both depend on the reference frame —Preceding unsigned comment added by 79.76.144.62 (talk) 02:19, 17 March 2008 (UTC)

DBasing the money supply
Wouldn't it be possible to enter the serial numbers that are already on US currency into a database, record the serial numbers of any currency that is stolen in the DB, scan all bills whenever they are tendered at a business and run a database check, and thus instantly know when any stolen money is tendered ? The weak point in the chain seems to be getting businesses to pay for the devices, but I imagine some tax incentive could be offered to get them to agree. StuRat (talk) 17:21, 16 March 2008 (UTC)


 * Such a system could easily be built based not on a piece of new equipment but merely on the upload of a digital picture of a bill using a regular scanner. This would also help everyone including the Secret Service to determining which bills were counterfeit. If yours turned out to be counterfeit then of course you would be stuck with the loss unless you could spend it quickly somewhere a scanner was not in use and the system did not require your name and to turn in the bill if it was found not to be legitimate. —Preceding unsigned comment added by 71.100.174.10 (talk) 17:43, 16 March 2008 (UTC)


 * I don't quite understand what you mean, StuRat. What is preventing the counterfeiter from copying legitimate serial numbers onto fake bank notes?  --Bowlhover 18:01, 16 March 2008 (UTC)


 * Serial numbers are unique and associated with other components of a bill which can not be duplicated exactly. Pictures of every bill issued already exist. Of two bills with the same serial number figuring out which one is real and which one is not is a relatively insignificant problem. —Preceding unsigned comment added by 71.100.174.10 (talk) 18:11, 16 March 2008 (UTC)


 * I was talking about the theft of valid money, not countefeit money. However, the system could be somewhat useful in apprehending counterfeiters, too.  If, for example, somebody tries to spend a large amount of currency and several of the serial numbers are listed as being in the possession of other banks and businesses, it might look suspicious and security might want to detain the big spender until the police arrive. StuRat (talk) 18:38, 16 March 2008 (UTC)


 * The potential cost of maintaining and using a database and a system that would hold information for all of the billions of US bills in circulation would be prohibitive and probably outweigh whatever is lost in counterfeiting. The labor required to enter in every bill one received and, presumably, all of the bills that one gave out (how else would you know which ones were stolen?) would be unreasonably large. Is it possible? Yes, sure. But wildly impractical. There's no way the gains would be worth the costs. --98.217.8.46 (talk) 18:02, 16 March 2008 (UTC)


 * And just to illustrate: say I run a business, even one that deals with a relatively small amount of money, like a convenience store. Let's pretend I have an automated machine that'll scan all of the money I put into the till, and registers it in some sort of giganormous Treasury database which always works (despite store millions of new transaction entries a day from around the country) and is miraculously fast enough to not make every bill check take as long as a credit card takes to process (about 10 seconds a card swipe or so, so if you paid for a $5 item in ones then you've got to sit around for a minute). (And note: yes, the business WOULD need to check with the centralized database every time they received a bill for change, because they too are also in the process of looking for "stolen" money from other businesses, right?) OK—best case scenario so far?
 * Now a customer comes, and I have to take the money they give me, scan it, and then take the money I give them, and scan it. Because I don't keep track of what I've taken out of the till, when my store gets robbed, I won't be able to distinguish between "valid" money that I gave out as a change and "stolen" money. Let's even pretend that this was somehow practical, and the system says that a mile away, someone put one of my five dollar bills into a till at a grocery store. The police are called, the suspect kindly waits for them to arrive, and everybody has a nice conversation about where that five dollar bill came from. Maybe, in an ideal world, the suspect matches a perfect description from the robbed cashier, they put him in a line-up, they identify him, they convict him. Bravo. But what if he doesn't match? What if, say, he got the five dollar bill from someone else? OK, now we've got a complicated situation here—maybe we try to shake him down and find out where he got that bill from. And so on and so on. The question is: how many times do you have to "catch" the wrong person for 1. people to think this is a waste of time, 2. businesses to think this is a waste of resources, 3. law enforcement to think this is a waste of resources? Not many. --98.217.8.46 (talk) 18:07, 16 March 2008 (UTC)


 * Okay you want special equipment. NCR can build a cash register with a bill scanner inside above the drawer. You put the bill in the drawer and the cash register does the rest. As for a waste of time... such a system has the potential to waste a crook's time rather than the police by simply going the extra step of requiring validation of the bill before it can be spent. Bill gets stolen the system is notified by pressing the "theft" key and poof the bill is no longer valid until re-certified by the police. —Preceding unsigned comment added by 71.100.174.10 (talk) 18:16, 16 March 2008 (UTC)


 * There is the voluntary project, http://wheresgeorge.com -- k a i n a w &trade; 18:17, 16 March 2008 (UTC)


 * Too many holes to be worth the effort. —Preceding unsigned comment added by 71.100.174.10 (talk) 18:23, 16 March 2008 (UTC)


 * Still a ridiculous suggestion. Do you think the police want to spend their time becoming "bill re-certifiers"? No law enforcement agency in the world is going to want to take on that task. The best way to catch criminals involves talking to other people, looking at specific forensic, not trying to track down each and every physical dollar. --98.217.8.46 (talk) 20:28, 16 March 2008 (UTC)


 * Thanks for confirming everyone's concept of the police as worthless lazy donut eating taxpayer supported freeloaders and do nothings until the opportunity arises to write a parking ticket or a ticket for driving near enough to the speed limit that in their minds it might as well be speeding. Not to mention being self-righteous oppressors of Berkley student freedoms. —Preceding unsigned comment added by 71.100.174.10 (talk) 20:57, 16 March 2008 (UTC)


 * I tend to think of police that way myself, as the only interaction I seem to ever have with them is when they extort money from me via tickets. Since I am neither a pretty woman good at flirting nor another policeman or government official immune to traffic laws, I never get out of a ticket, either.  When anyone is driving like a fool and actually endangering lives, no police are ever to be found.  I even saw one instance where police apparently put up a barracade and stopped traffic with the sole purpose of ticketing those who drove around it.  StuRat (talk) 22:30, 16 March 2008 (UTC)


 * Many of the limitations listed are only current limitations, which can hopefully be solved soon. I've never understood why credit card approval takes so long, and increasing bandwidth, etc., should make this process quicker soon.  Also, rather than "dialing in" for each bill, something like a DSL system can be always on and ready for a check.  Looking up a unique serial number in a database is one of the quickest DB operations there is.  Initially, perhaps only banks would record the location and distibution of currency, with businesses merely running a check, not updating the database.  A few years later on, businesses could update the records, too.  Note that the full system could also be used as an anti-terrorism tool, as terrorists often need to move large sums of money around.  If they go to a bank and withdraw large sums of money, the serial numbers could be tracked and we would know, say, if they used it to buy weapons and explosives.  It would also be interesting to know if large sums of money given to Islamic charities are being used to purchase weapons. StuRat (talk) 18:50, 16 March 2008 (UTC)


 * The whole thing is totally impractical with paper money. And at least in the United States, no arms dealers are going to start using such a system—a lot of the transactions would be "off the grid", especially for those involving potentially scandalous or illegal activities. There are better ways to check how businesses and charities spend their money if one is inclined to do so.
 * It doesn't matter whether reading the index of a bill is a quick operation—even a relatively quick operation needs to be able to scale. And every complex system is going to have major downtimes, bugs, etc. in it.
 * My money (haw haw) would be on using electronic money and getting rid of paper money long before any of this would ever become practical, and I still think that even if you did have a system of tracking paper money it would still be wildly impractical. Certainly more impractical than just making everyone switch to purely electronic currency and skipping the paper step altogether. If countries make universal IDs mandatory (which I suspect they will in the next decade or so), that would make it all the easier. --98.217.8.46 (talk) 20:24, 16 March 2008 (UTC)


 * Certain "high-risk" businesses, like gun shops, pawn shops, etc., could be forced to comply by law. It would be easy enough to verify, just have an undercover cop go in with a "bad bill" occasionally, and, if they don't report it and refuse to sell the gun, give them a whopping huge fine.  This method would allow the police to make a nice profit, ensuring that they would actually enforce the law.  StuRat (talk) 22:21, 16 March 2008 (UTC)


 * (And if you're worried about people buying guns, why not make them register the guns? There are far less guns than dollars, and they're much larger, much more worth the effort. If you think people don't want you to track their gun-buying habits, or that they can find ways around that check, why would you assume money would be any easier?) --98.217.8.46 (talk) 20:30, 16 March 2008 (UTC)


 * People don't usually leave guns around after a crime. And, if they want to get around the tracking, it's a lot easier to remove a serial number from a gun than from every bill you ever have. StuRat (talk) 22:12, 16 March 2008 (UTC)


 * What has been learned from previous experiments to track money is that criminals create their own from of money and find other ways to thwart tracking like through the construction, purchase and sale of real estate. A "company" buys a lot for twice what it is worth, builds on it and sells the lot and the building for eight times the going price of any adjacent property. People are so open to a free market under capitalism they do not even bat an eye. Money gets laundered like this around here all of the time and no even cares.


 * This might help track down the laundering operations, too. If an armored car is robbed, then, a year later, somebody buys a $100,000 home for $200,000 in cash, and many of the bills are those stolen from the armored car, the buyer would have some explaining to do. StuRat (talk) 22:15, 16 March 2008 (UTC)


 * Why would you assume that they'd be using that money anyway? If a ridiculous tracking system went into effect, what's to prevent someone going outside of the country to launder it? You severely overestimate the technical abilities needed to do such a thing while at the same time you underestimate how easy it would be to get outside of the grid. Again, there's nothing your system would offer that a generalized electronic money system would not, except that yours would cost billions more to produce and maintain in both infrastructure costs and operation time, and because you still were trying to rely on physical money you make it exceptionally easy to evade your proposed system. In any case, armored cars are not robbed all that often and the companies that run them are insured anyway (you're using a very clunky hammer to try and hit a pin of a problem). --98.217.8.46 (talk) 00:55, 17 March 2008 (UTC)


 * Moving currency offshore in large quantities has it's risks, too, as anyone repeatedly smuggling large sums of cash is likely to be caught. The armored car was just an example, it doesn't really matter where the currency was obtained illegally.  And, whether they are insured or not is quite irrelevant, it only means the insurance company now wants the cash recovered instead of the original target. StuRat (talk) 01:07, 17 March 2008 (UTC)

Interesting question, StuRat, but lets take the suggestion even a step further: Looked upon this way, your proposed system is just an insufficiently ambitious version of an all electronic financial system, which (in developed countries at least) accounts for (guesstimate) 99.9...% of all financial transactions (once we account for all financial activities, i.e., not only retail consumer purchases). Aside: We may well be living in the the last-few-decades of the physical currency era, and future generations may look back with amusement and disbelief at our primitiveness, just as we consider a barter economy obsolete and limited. PS: The only relevant wikipedia article I could find is the one on electronic commerce but the scope of that is too narrow for our discussion. Abecedare (talk) 02:22, 17 March 2008 (UTC)
 * Instead of carrying paper currency around, why don't we store the serial numbers of the currency that each person owns in a (verifiable and secure) database.
 * Then instead of presenting the paper bills to (say) a gun shop, one only needs to provide a secure ID and the database is remotely updated to transfer ownership records of the requisite amount of paper currency.
 * As a last step, clearly we don't need to store the actual "serial numbers" of the notional "paper" money, but only the amount of money that each person possesses at any particular point of time.


 * I don't agree with 99.9% of all transactions being electronic. Perhaps if measured by percentage of total transaction value, that would be correct, but many small transactions, like fast food restaurants, paying the paper boy, etc., still are largely done with cash.  In a society without cash, bums would have a hard time getting a hand-out, too (I picture them carrying a credit card scanner to accept donations :-)).  I, for one, use cash whenever possible, as there is no possibility of ID theft when I hand the cashier cash (and if a cashier doesn't take cash, do they become a "creditier" ?). StuRat (talk) 05:31, 17 March 2008 (UTC)
 * Yes, I meant 99.9...% by value (I'd be curious to know the true stats).
 * The bum wouldn't have to carry credit card scanners. All you'll need to do is note down their Database ID number (perhaps, their ID card will communicate wirelessly with your "mobile phone") and transfer funds electronically to their account, which they can then access instantaneously. Note that this perfectly implementable using today's technology, although clearly there are sociological, economic, ID theft and other non-technological issues. IIRC, on several university campuses one can pay petty expenses, such as vending machines, laundry etc using the student ID card and that may be a first step towards a cashless society with all its benefits and ills.
 * Cheers. Abecedare (talk) 06:01, 17 March 2008 (UTC)


 * An interesting effect of a cashless society would be that it might force many back to a barter economy. An illegal immigrant likely can't use a credit card, so, without cash, they would need to be paid in room and board and maybe pesos, if they weren't also eliminated. StuRat (talk) 19:31, 17 March 2008 (UTC)


 * Again hardened criminals and just ordinary people who want to avoid paying income and sales taxes barter all of the time without cash or debit cards getting involved. You sell a house to someone for $950,000 no one is going to require you to show where they actually paid or where you actually deposited the cash. Instead the house can be a payment in reality rather than a sale. You can avoid the grid without going offshore and by staying right here. Everyone knows how to work the system and how the system works. —Preceding unsigned comment added by 71.100.174.10 (talk) 09:30, 17 March 2008 (UTC)

artificially macerated food
As an informal experiment I have been macerating my meals using a food processor. The consistency of maceration is about the same as bean dip used for tacos but includes meats, vegetables and most components of a regular meal including condiments. I consume a beverage with the macerated meal. Not only do I become full with only half a meal but have been able to reduce the number of meals to one per day with occasional in between unmacerated light snacks. Not only do I seem to have more stamina for excercise but the pounds are beginning to come off. Where can I find scientific or medical studies which discuss artificially macerated food? —Preceding unsigned comment added by 71.100.174.10 (talk) 17:34, 16 March 2008 (UTC)


 * The only way I can see that helping is if the food is less palatble in that form, so you eat less of it. StuRat (talk) 18:54, 16 March 2008 (UTC)


 * It is somewhat less palatable but not to a degree that it is something one can not get use to in light of other benefits. What I need is a list of studies which have explored the question in depth. —Preceding unsigned comment added by 71.100.174.10 (talk) 21:14, 16 March 2008 (UTC)


 * I'm not aware of any studies. But what exactly would be the mechanism by which you would desire to eat less, if not that the food is unpalatable ?  I suppose that might still be better than diet/weight loss methods like Alli, which apparently causes weight loss because people who take it crap their pants unless they stop eating fat.  Talk about unpalatable ! StuRat (talk) 22:03, 16 March 2008 (UTC)
 * ...you know perhaps NASA has a study. I just thought of that. Even Stanley Kubrick included it (pre-macerated food) in his film. —Preceding unsigned comment added by 71.100.174.10 (talk) 09:13, 17 March 2008 (UTC)


 * Check with aged-care studies, where macerated food (often reset in more attractive moulds) is used.Polypipe Wrangler (talk) —Preceding comment was added at 23:34, 16 March 2008 (UTC)


 * This question sounds strikingly familiar. --The Fat Man Who Never Came Back (talk) 23:58, 16 March 2008 (UTC):-)
 * Weathermen are notorious for earning good livings by giving different answers to the same questions every day. —Preceding unsigned comment added by 71.100.174.10 (talk) 08:55, 17 March 2008 (UTC)

How much human evolution is yet to come?
Is there any evidence regarding how close human evolution is to reaching an end state where it will stay? How much improvement is left to be made over the next few million years, assuming the planet remains habitable that long? Neon Merlin  18:22, 16 March 2008 (UTC)


 * That's easy. Whatever will make the human physically and mentally more efficient. An adaptation to the ever increasing abundance of pornography, for instance, might be a third hand growing out of one's thigh. ;D —Preceding unsigned comment added by 71.100.174.10 (talk) 18:25, 16 March 2008 (UTC)


 * As long as the environment changes, evolution will cause change in the species that survive. Even if the environment on Earth becomes static (which is not likely), humans are trying to go to other planets, which will lead to evolution to match the foreign environment. --  k a i n a w &trade; 18:41, 16 March 2008 (UTC)


 * Unfortunately, human evolution is likely to take a nasty turn, where those who irresponsibly produce the most children and abandon them are likely to pass on the most genes. Historically, the abandoned children would die, but in modern society, they are taken care of by the state.  In the long run, however, the state will no longer be able to care for the expanding pool of abandoned children, and they will no longer survive.  Or, perhaps before we get to that point, some fairly radical solutions, like forced sterilization, will become acceptable. StuRat (talk) 19:00, 16 March 2008 (UTC)


 * By chance, Stu, have you seen Idiocracy? Someguy1221 (talk) 20:36, 16 March 2008 (UTC)


 * No, I haven't, since doing so won't tend to increase the number of times I reproduce. :-) StuRat (talk) 21:53, 16 March 2008 (UTC)
 * And spending time on Wikipedia does? o_O Someguy1221 (talk) 23:38, 16 March 2008 (UTC)
 * Irresponsibility is not a genetic trait. There's no reason to assume those particular children are going to be any stupider than others. The complaint about "abandoned children" (or the mentally disabled, or the physically disabled) overburdening the state has been a nice scare fantasy of eugenicists for over 100 years now; the state seems to be doing just fine in that respect. It is pretty unlikely that compulsory sterilization will ever become in vogue again in Western countries. --98.217.8.46 (talk) 20:20, 16 March 2008 (UTC)


 * I don't agree that irresponsibility isn't a genetic trait (the Kennedy family may make my point for me). But, even if we say it isn't, children who are abandoned are also less likely to grow up to be responsible parents due to the lack of a good role model.  As for abandoned children being cared for "just fine", this certainly isn't the case.  In Romania, for example, they have a high fatality rate in underfunded and often abusive state-run institutions.  The kids are often misdiagnosed as having severe mental and physical problems, which, while not true initially, becomes a self-fulfilling prophecy the longer they remain there.  For example, since they are judged incapable of learning, they aren't given access to education, which, in turn, leaves them illiterate.  The story isn't much better in the US, where children are often shuffled from foster home to home, some of which are abusive.  Also, 100 years is an insignificant amount of time on the scale of human evolution, so I'm not surprised that the negative aspects haven't yet become overwhelmingly apparent.  StuRat (talk) 21:47, 16 March 2008 (UTC)


 * I say "just fine" from the standpoint of the species and the standpoint of the survival of the state. This is a conversation about evolution, right? Abandoned children make up an insignificant part of the human gene pool, as does all of Romania. Even the United States doesn't stand for a whole lot on a biological level. If you want to talk about biology, talk about biology. If you want to talk about society, okay, talk about society. But don't pretend you are talking about one thing when you're talking about the other. For all of your talk about the effects of modern society on the long-term prospects of the human species, your views are tailored to very small issues and completely absent are any considerations that would take into account, say, the most populous societies on the planet. Don't wrap your ideology up in scientific terms and pretend it is science—that's another bad legacy of the eugenicists for you to avoid. --98.217.8.46 (talk) 00:51, 17 March 2008 (UTC)


 * When did I say Romania and the US were the only countries having trouble caring for abandoned children ? It's a problem in many countries.  If you want to wait until we get to the point where nearly all abandoned children die to see it as a problem, then it will be too late to avoid the worst consequences by then. StuRat (talk) 01:22, 17 March 2008 (UTC)


 * You might be interested in the higher evolution.--Shantavira|feed me 19:23, 16 March 2008 (UTC)


 * I won't argue StuRat on intellectual grounds but I may say that his view strikes me as a touch pessimistic.


 * As to the original question, a quote from Hagakure:


 * A certain swordsman in his declining years said the following:


 * In one's life, there are levels in the pursuit of study. In the lowest level, a person studies but nothing comes of it, and he feels that both he and others are unskillful. At this point he is worthless. In the middle level he is still useless but is aware of his own insufficiencies and can also see the insufficiencies of others. In a higher level he has pride concerning his own ability, rejoices in praise from others, and laments the lack of ability in his fellows. This man has worth. In the highest level a man has the look of knowing nothing.


 * These are the levels in general. But there is one transcending level, and this is the most excellent of all. This person is aware of the endlessness of entering deeply into a certain Way arid never thinks of himself as having finished. He truly knows his own insufficiencies and never in his whole life thinks that he has succeeded. He has no thoughts of pride but with self-abasement knows the Way to the end. It is said that Master Yagyu once remarked, "I do not know the way to defeat others, but the way to defeat myself. 


 * Throughout your life advance daily, becoming more skillful than yesterday, more skillful than today. This is never-ending.


 * I believe this to be true at the level of the human race as well as the individual. So, to answer the question with this in mind: there is no end-point in human evolution. Vranak (talk) 19:31, 16 March 2008 (UTC)


 * The question as to whether humans will keep evolving in a meaningful way (that is, having more than just incidental circulation of gene frequencies, etc.) and whether that will be for the better or the worst has been asked since the 19th-century. There isn't really a single right answer for it. Human selective pressures have been relatively weak on average for a long time now—we don't tend to let people die off who might otherwise, and no individuals tend to have trouble reproducing if that's what they want to do. Human genetics and human society are both sufficiently complex that the Social Darwinist beliefs that those with money/power/affluence must necessarily be genetically "superior" to those without them have long been shown to be very flawed. There is also the big question of human genetic engineering, which could lead into a variety of different possible directions. Lee Silver's book Remaking Eden suggests a number of interesting possibilities in it without making terribly large assumptions about the scientific advances needed. --98.217.8.46 (talk) 20:20, 16 March 2008 (UTC)


 * Assuming machines keep on tending to make life easier and humans do not suddenly come under some sort of drastic survival pressure, then any changes that occur will not be considered improvements by most of us. For instance, lack of toes will not instantly result in death or the inability to reproduce.  It might have been so once upon a time, but not now.  What is going to stop evolution getting rid of toes if they have no survival benefit?  Or take our precious brains, very expensive in energy to maintain, but no survival value now that we have machines to do all our thinking for us.  Probably first thing to go if evolution needs to save on energy for any reason.  We will only be saved from this terrible future if survival becomes more difficult, or cosmetic genetic engineering becomes legal and cheap.  Sp in ni  ng  Spark  20:33, 16 March 2008 (UTC)


 * If there is no selection for a trait then it's not going to propagate. And I don't know about you but my machines haven't learned to do any thinking for us; so far, all predictions of human intelligence being useless have proved pretty baseless. At the moment, for all of your fears of brains being cosmetic, most of our top paid professions require big brains, ergo the difficulty of getting into and succeeding in law school, business school, medical school, etc. If anything has characterized human society in the last hundred years it has been the increased importance of expertise and the slow shuffling towards something of a meritocracy (as opposed to the centuries of hard and fast rule by aristocracy). I wouldn't be all that worried.


 * As for toes, if there is no strong selective pressure for it, it won't catch on. You might think there is not selective pressure against it, but I'm betting that most toe-less individuals would probably disagree to some extent. And in any case, sometimes there is a benefit to missing a few. ;-)


 * Evolution and genetics is much more complicated than the "toes" example, in any case. Evolution in the face of heavy selective pressures can be quick in small populations, but in a very large population with a lack of selective pressures I think you're going to find mostly a regression towards the mean on the whole, e.g. not much change in either direction over the course of the population as a whole. (Ironically, that is what the founder of eugenics, Francis Galton, thought too. He thought this was stagnation. I consider it just to be stability.) --98.217.8.46 (talk) 20:41, 16 March 2008 (UTC)


 * Humans and the demands of their environments are quite mobile. Adaptation often takes the form of simply moving to a place where your deficiencies become meaningless and your talents are irreplaceable. Hence, Lovette goes to jail, Hilary and Barack hit the campaign trail and McCain heads for Iraq. —Preceding unsigned comment added by 71.100.174.10 (talk) 21:27, 16 March 2008 (UTC)


 * Yes it's true that brains are still valued in law, science and medicine etc. but my point is that this makes no difference to an individuals abililty to procreate. Hence, it is irrelevant to evolution.  The unemployed make just as many children as brain surgeons, possibly more.  Sp in ni  ng  Spark  21:45, 16 March 2008 (UTC)


 * Money appears to be the deciding factor when it comes to procreation even for the lowest class rather than brains unless brains translate into money. —Preceding unsigned comment added by 71.100.174.10 (talk) 21:56, 16 March 2008 (UTC)

Biological evolution is an ever ongoing incessant process. It occurred in the past, is occurring at the present, and will continue to do so in the future as long as life exists on the planet.  Wisdom89  ( T |undefined /  C ) 22:22, 16 March 2008 (UTC)

The only end state for evolution of humanity will be extinction or immortality. If you agree with the Doomsday argument the former may be quite soon. GameKeeper (talk) 23:28, 16 March 2008 (UTC)


 * Extinction is the only eventual possibility, the question is when and why. Personally I'm of the "we're never going to get off of this hunk of rock" school of thought, and would be highly surprised if we made it through the next century, judging by how the last one went. --Fastfission (talk) 23:38, 16 March 2008 (UTC)

One recent study found that human evolution had recently accelerated (though "recently here" is from 50,000 BC to 10,000 BC or so). 140.247.254.4 (talk) 01:03, 17 March 2008 (UTC) We could also be in a state of de-evolution now that computers are handling so many of our former jobs.
 * Assuming a distant stable future and an extreme mastery of technology and genetic manipulations by the descendents of humans, we can imagine a world where the idea of human evolution as become obsolete. An almost total ability to genetically engineer and transform organisms breaks the barriers between what we call robots and living organism. The notion of 'humanity' has lost its meaning as it has become only a narrow range of genetic possibilities in a large spectrum of possible configurations that are all part of society, or maybe the term's meaning has broaden to include all sentient beings. So the idea of human evolution will disappear in time to be replaced by genetic engineering (and maybe we'll all look like manga and disney characters?). Keria (talk) 13:30, 17 March 2008 (UTC)


 * It bears mention that we haven't really been around as a species for all that long. The numbers are hard to imagine as they are -- 2.5 Million Years for humans and 3.8 billion years for the cooled planet -- but consider the first land masses on earth as having formed around midnight of January 1, and we are approaching midnight of Dec 31 a year later.  That puts humans on the planet for the past 4 ½ hrs -- during the first two hours of which we seemed to coexist quite peacefully with the Neandertal, and possibly others.  All of recorded history has taken place in the past 2 minutes.  (The dinosaurs died out on Christmas Eve).  The jellyfish, in contrast, have been around for a couple of months, relatively unchanged.  In the face of these kind of numbers, it's easy to see where the question gets murky.  If we are to quantifiably evolve, it's going to take tens of thousands of years, just like every other organism on the planet, which means that we've got to survive long enough to do it.  And if we're talking about a speciation event, then by definition "we" will no longer be...Vance.mcpherson (talk) 21:42, 17 March 2008 (UTC)


 * It also bears mention that evolution of the traditional sort is likely soon to be made insignificant in copmarison to artificial, intentional tinkering. &mdash;Tamfang (talk) 23:21, 19 March 2008 (UTC)


 * Technological singularity seems to have a great chance to occur a lot sooner than any detectable biological evolution. --V. Szabolcs (talk) 14:30, 22 March 2008 (UTC)

Winter Solstice
In the year 1990, did the winter solstice fall on December 22nd? Or the 21st? 71.174.25.42 (talk)Winter


 * The winter solstice falls on the 21st during leap years and the 22nd during regular years. 1990 was not a leap year.  Therefore, December 22 was the winter solstice.  --Bowlhover 21:40, 16 March 2008 (UTC)


 * Unfortunately, it's not quite that simple: "Depending on the shift of the calendar, the event of the Winter solstice occurs some time between December 20 and December 23 each year in the Northern hemisphere." See Winter Solstice, especially the graph on the left. You also need to keep in mind that the solstice proper is a single moment, which happens simultaneously in all time zones. Depending on where on the planet you are, it may be late in the evening on one day, or early in the morning on the next. BTW, (found through Google) gives the 1990 winter solstice happening on Dec 22 at 03:10 UTC. Note that this is actually 9:10 pm on Dec 21 in Chicago. (Also note that the Winter Solstice happens in June for those people south of the equator, due to the inversion of the seasons:) -- 128.104.112.85 (talk) 22:49, 16 March 2008 (UTC)


 * For some reason, I thought the winter solstice always fell on December 22 UTC time or December 21 UTC time. Of course, that's not true; the winter solstice article states that it occurs on December 20 this year and December 21 for a few years afterwards.  --Bowlhover 04:22, 17 March 2008 (UTC)

Radiography in Thailand?
Does anyone have any information on working as a radiographer in Thailand? I am studying it at the moment in Scotland and would quite like to do an elective placement there. 172.142.123.129 (talk) 23:02, 16 March 2008 (UTC)
 * I had a look, and curiously we don't have a Healthcare in Thailand article. Perhaps the best place to start would be the Thai Embassy in London which has a list of hospitals in Bangkok.  Sorry, I couldn't find out if there was a consulate in Edinburgh.  Astronaut (talk) 04:21, 18 March 2008 (UTC)

what is the most effective toothpaste?
which brand of toothpaste is the most effective? —Preceding unsigned comment added by 79.122.42.52 (talk) 23:40, 16 March 2008 (UTC)


 * The brand you actually use. —Preceding unsigned comment added by 71.100.174.10 (talk) 23:44, 16 March 2008 (UTC)


 * That would depend on what you want it to do. There is cavity prevention, tartar control, tooth whitening, fresh breath, etc.  Depending on what particular problem(s) you have, a different formulation may help. StuRat (talk) 23:53, 16 March 2008 (UTC)


 * The one that claimed to be able to split water molecules during brushing in order to release 'activated oxygen' into the mouth for a deeper clean sounded pretty interesting. Shame they stopped advertising it... --Kurt Shaped Box (talk) 23:58, 16 March 2008 (UTC)
 * All you need to do that is brush with hydrogen peroxide. —Preceding unsigned comment added by 71.100.174.10 (talk) 00:02, 17 March 2008 (UTC)

I'm not sure what brands are available in Hungary, but you might want to check out an independent product reviewer like ConsumerReports.org, or even a website like Epinions.--The Fat Man Who Never Came Back (talk) 23:54, 16 March 2008 (UTC)

All of the same major ones are available here as the US. Which is the best? (Did you read independent reviews?)


 * As you haven't said exactly what you mean by "most effective", you might do well to read the Consumer Reports' article on various aspects of toothpastes and the claims made about them here . ៛ Bielle (talk) 01:35, 17 March 2008 (UTC)
 * I had a small travel pack of Colgate sensitive (clinically proven sensitivity relief) promising all kinds of protection and relief from pain, which I used to clean the grunge off the baked enamel stove top -- surprisingly effective. No need for harsh scrubbiing. I'm still waiting to hear from the cooker about its new found confidence, but I'm keeping it handy for next time when nothing else works. Julia Rossi (talk) 05:23, 17 March 2008 (UTC)

please remember that the most effective toothpaste always has most number of active chemicals which means you may.. may..and not definitely.. damage your teeth. So, I always prefer the least effective from a trusted company. -Balaji —Preceding unsigned comment added by 59.92.126.151 (talk) 13:58, 18 March 2008 (UTC)

Speed in space(not the drug)
I was discussing with a friend about the age of the universe. A subject way over my head. I brought up that a quasar had been found that was 28 billion light years away from us and gaining. Yet the universe is only 13.73 billion years old. So that would mean that the quasar is traveling faster than the speed of light. It has moved farther than light could in that time. Disance in time = speed.(I know that we are also moving, so some math would have to be done) That is how I and the traffic cops understand speed. But he said that it realy was not moving that fast. The space in between us was actualy growing. My response was Duh, you don't say. That is what distance is. Anyway, he was serrious. He said I would have to understand general reletivity to understand that objects in space are not moving at speed but that space was growing. Can you tell me if he is an idiot or not? And if he is not can you explain this in common language? thanks.

cris —Preceding unsigned comment added by 68.209.69.103 (talk) 23:59, 16 March 2008 (UTC)


 * Metric expansion of space, yes, space is in fact getting bigger. A common analogy used in popular science it to imagine a universe that is confined to the surface of a balloon. The balloon obviously has a volume to it, but everything, including light, is permanently stuck to travelling along the surface. If you draw two dots on the balloon to represent, say, you and a quasar, and then you blow up the balloon, you two will get farther and farther apart. Each of you can look around and accurately say, "Everything around me is moving away from me, and I seem to be standing still." So who's right, and who's moving? Or is it merely space that's changing? I'm not a general relativity expert, so that's as close as I'm going to get to explaining this to you. Someguy1221 (talk) 00:08, 17 March 2008 (UTC)

OK. I understand the baloon analogy. But the two objects are still gaining distance from one another. Wouldn't that still asign speed to them? Are all objects in space spreading apart? Are they doing this equaly or are some moving faster away than others? —Preceding unsigned comment added by Loach (talk • contribs) 01:18, 17 March 2008 (UTC)


 * I removed the spaces from before your answer, because they put your text in an unformatted grey box ...

like this.
 * If you want to indent text, use colons (these things - :::::) instead. Now, on to your question. Yes you can assign a speed to the separation between two objects, but there are two caveats: (1) you can only say that they're moving relative to each other, and (2) you do so based on the frame of reference you are observing from. The "relativity" in Einstein's theory of relativity refers to the fact that as long as you keep track of things properly, no frame of reference is better than another - and most importantly, there's no "true" frame of reference, so you can't just say "that object is moving at this velocity" unless you state with respect to what. As to the rest of your questions, yes most of the observable universe appears to be expanding at a fairly uniform rate, with differences due mostly to gravitational effects (if you and I are standing on the balloon, and holding on to each other, then we won't be pulled apart as much as the balloon expands). In fact, the uniform expansion of space is what allows us to equate how far away things are with how fast they're moving away from us, proportional to Hubble's constant. And that linear relationship means that, yes, the furthest objects appear to recede faster than the speed of light. Confusing Manifestation (Say hi!) 03:03, 17 March 2008 (UTC)
 * There are no inertial reference frames at cosmological scales; the symmetry is broken by the overall curvature. Length contraction, time dilation and the relativity of simultaneity are meaningless in cosmology. There is a privileged time coordinate (cosmological time, the distance to the south pole on the globe below) and a privileged spatial distance (comoving distance, the difference in longitude on the globe), which can be used to define a privileged recession velocity between two objects. Hubble's law says that the (privileged) recession velocity is roughly proportional to the (privileged) distance. There is no privileged position or absolute velocity, though (i.e. no center to the expansion). -- BenRG (talk) 21:36, 17 March 2008 (UTC)

OK. Sorry for the grey box. I do not know how I did that. One last question. Does the universe have a central starting point from which the BB started? I've heard both yes and no. Do we know where it is? And could a reference on speed be made from there. thank you for your help. —Preceding unsigned comment added by 68.209.69.103 (talk) 03:29, 17 March 2008 (UTC)


 * You're probably hitting TAB or something before typing your questions. Anyway, there was no central starting point. If you were to run the universe backwards, and watch it with a camera in any inertial reference frame you please, you would see the density of the universe climb higher and higher, approaching infinity at the big bang. Once again, this would happen no matter where your camera was or what reference frame your camera was in. So every position in space has equal claim to having been the "central starting place." And depending on what the shape of the universe is, the universe may well have always had infinite volume and no boundaries; so it may actually be geometrically impossible to define a center of the universe. Someguy1221 (talk) 03:39, 17 March 2008 (UTC)
 * See my response above—no inertial reference frames. Also, it doesn't make sense to say that something is in a particular inertial frame, since every inertial frame assigns coordinates to every object. Also also, the universe doesn't look the same at different speeds (it makes a difference whether you're moving with respect to the CMBR). But it's true that the camera will see the density go to infinity regardless of its state of motion. -- BenRG (talk) 21:36, 17 March 2008 (UTC)


 * It's not just that objects are moving (which they are); the very fabric of space is expanding as well. Imagine two ants on a blanket, walking away from each other. But the blanket itself is also stretching wider at the same time, so the net distance that they are from each other increases very quickly. What's impressive is that this particular effect—the expansion of space—is pretty much the only way that something can end up going faster than the speed of light relative to anything else. The objects themselves are not moving faster than the speed of light, but the distance between them is growing at a rate that they end up distances apart that would require going faster than light to actually have done had the space not been expanding. Crazy, no? --98.217.8.46 (talk) 14:18, 17 March 2008 (UTC)


 * How can we see something farther than n light years away when the universe is only n years old? That's easy: it's simply not true that light travels a distance ct in a time t. It's never been true, thousands of confident assertions in books notwithstanding. [[Image:Loxodrome-1.gif|right]]It's easiest to visualize what's going on in the case of a closed universe which expands, reaches a maximum size, and then recollapses. For simplicity suppose there's just one spatial dimension, which is all we need for this example. You can imagine this universe as the surface of a globe, with the south pole being the big bang, the equator being the time of maximum size, and the north pole being the big crunch. (Note that this is different from the "expanding balloon" analogy—this is a fixed-size balloon which shows the whole history of the universe at once.) We can draw lines of latitude (x axes, purple) and lines of longitude (t axes, cyan) on this globe. We'll draw a very large number of them so that the whole globe is covered fairly densely with intersecting latitude and longitude lines. What "light travels at a constant speed" really means is that light crosses all of these intersecting axes at the same angle. Usually the units are chosen so that the angle is 45°. A curve with this property is known as a loxodrome, and an example is shown in white in the image to the right. Unfortunately the angle here is nowhere near 45°, but try to imagine a similar curve with a 45° angle. Say that the present era is 30° from the south pole. The spatial size of the universe in this era is 2πR sin 30° = πR, and the elapsed time since the big bang is πR/6, where R is the radius of the globe. The first question is: how far away in this era can two objects be that started out in the same place at the big bang, and that have moved slower than light since then? The answer is obviously "arbitrarily far". In particular, they can be on opposite sides of the universe (πR/2 light years apart) even though it has only been πR/6 years since the big bang. The second question is: how far away is the most distant object we can see? The answer is again "arbitrarily far", because the loxodrome that represents the path of a light beam has circled the entire universe in the time since the big bang. In fact it has circled it infinitely many times, so we will see infinitely many images of everything in the universe at progressively earlier stages in their evolution. Note that the distances involved here have nothing to do with the speed c—they're a consequence of the large-scale geometry. The distance ct, where t is the time since the big bang, is geometrically meaningless. In the real world, the current distance to the south pole (along a line of longitude) is 13.7 billion years, and the current distance to the most distant known quasar (along a line of latitude) is 28 billion light years. Nothing in the geometry of the real world relates the latter to c times the former.
 * The globe model differs from the real FLRW metric in a few ways. First, it's missing two spatial dimensions, but that doesn't matter here. Second, the scale factor is wrong: a(t) ~ sin t isn't even a solution of the Friedmann equations, much less a solution approximating the world we see. Third, there's no reason to think that the real universe wraps around spatially like that. You can imagine "unrolling" the globe such that circling around it actually takes you to a new place (technically this is taking the universal cover of the sphere with the poles removed). Fourth, the early universe was opaque, so we should actually cut off the loxodrome some distance short of the south pole (i.e. when it hits Antarctica). But the basic geometry is right. This is why we can see things farther than ct away. -- BenRG (talk) 21:18, 17 March 2008 (UTC)
 * Hi. I'm not really an expert at this but is it possible that the light left the quasar, say, 12 billion years ago, and travelled to us now, so the image is really only 12 billion light-years away, but people calculated it based on the redshift of the quasar, and perhaps estimated that the quasar is currently 28 billion light-years away from us, as the expansion of space can travel faster than light in all those dimentions but matter itelf relative to itself can't? Thanks. ~ A H  1 (TCU) 23:13, 17 March 2008 (UTC)
 * I'm not sure I understand your question. There is no image 12 billion light years away. As I said above (and below), the travel time times c is a completely meaningless distance. It has no physical significance at all. Light really does not travel 12 billion light years in 12 billion years. -- BenRG (talk) 23:57, 18 March 2008 (UTC)


 * Okay, I got inspired and made some numerically accurate images. These are two views of a surface that's just like the globe above except that the shape is calculated from the ΛCDM model and the WMAP five-year data. Click on either image for a larger version, and on the first one for some mathematical details of the embedding. The small circle at the "bottom" is 700 million years after the big bang. (Nothing earlier can be embedded with this particular choice of embedding parameters.) The large circle at the "top" is 18 billion years after the big bang, where you can start to see the accelerating expansion that eventually dominates in this model. The lines of latitude (purple) are 1 billion years apart. The lines of longitude (cyan) are one billion present-era light years apart. They're closer together than that in the past and farther apart in the future; in all eras the physical distance is proportional to the Euclidean distance measured along the lines of latitude. The cyan lines are also the worldlines of objects moving with the Hubble flow. The brown line is the worldline of the Milky Way and the yellow line is the worldline of the most distant known quasar with redshift z ~ 6.4 (I've assumed both are moving with the Hubble flow). The red line is the path of light from the quasar to present-day Earth, and the orange line shows the quasar's distance from Earth at the current cosmological time. You can verify by counting grid lines that the present-era distance to the quasar is about 28 billion light years and the light travel time is about 12 billion years. You should also be able to see that the light beam always makes a 45° angle with the nearby grid lines. (In the second image it kind of looks like it doesn't, but that's because of the perspective foreshortening.)


 * Every light beam currently reaching the earth follows the same path as the red beam, except possibly with an earlier or later starting time or from a different direction. So the region of spacetime we can see right now—that is, Earth's past light cone—is the subsurface traced out by the red line and its counterparts in other directions (most of which can't be drawn on this surface since two dimensions of space are missing).


 * Another interesting thing to notice is that the (real, metric) distance between the light beam and the Milky Way increases for the first few billion years before reaching a maximum and decreasing again. This is related to the odd fact that the angular diameter of extremely distant objects increases with distance—that is, the rules of perspective are reversed and more distant objects look larger. The cosmological time at which objects look smallest is the same as the time at which the light beam's distance is largest. The reason for this is left as an exercise for the reader (there's a simple geometrical answer).


 * I deliberately cut off the embedding short of a full circle to emphasize that space doesn't loop back on itself. The cutoff distance doesn't have any physical significance, and neither does the circumference of the full circle. It's an adjustable parameter of the embedding and I just picked a value that looked good.


 * All four of the colored lines are loxodromes (if that word is appropriate for a surface that's this much unlike a globe). The brown, red, and yellow lines are also spacetime geodesics, but the orange line isn't. N.B.: most geodesics are not loxodromes and most loxodromes are not geodesics. In fact they only coincide when v=0 or v=c, which happen to be the two cases that appear here. Also note that the spacetime geodesics (based on the real, Lorentzian geometry) are not the same as the Euclidean geodesics on this embedded surface, unfortunately. But I still think this kind of embedding is a useful way of understanding the expansion of the universe. It might be nice to have these images or similar ones in metric expansion of space. The expanding raisin bread model leaves something to be desired. -- BenRG (talk) 23:57, 18 March 2008 (UTC)
 * Holey-moley! Excellent detail, I'm bookmarking this for the future. I sure hope you're right, I'll be reading this for awhile :) Thanks for the effort! Franamax (talk) 00:17, 19 March 2008 (UTC)


 * Indeed! BenRG's analysis and explanation should definitely be preserved in an article.  Also, kudos to Confusing Manifestation for helping the new user edit as well as providing responses along with 98... and Someguy. Truly a noteworthy thread. --hydnjo talk 20:36, 21 March 2008 (UTC)